This note reformulates certain classical combinatorial duality theorems in the context of order lattices. For source-target networks, we generalize bottleneck path-cut and flow-cut duality results to edges with capaci...
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We present vector-valued concentration inequalities for the biased measure on the discrete hypercube {−1, 1}n with an optimal dependence on the bias parameter and the Rademacher type of the target Banach space. These ...
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We study a two-dimensional McKean-Vlasov stochastic differential equation, whose volatility coefficient depends on the conditional distribution of the second component with respect to the first component. We prove the...
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The dynamic behavior of RMSprop and Adam algorithms is studied through a combination of careful numerical experiments and theoretical explanations. Three types of qualitative features are observed in the training loss...
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This study evaluates the effectiveness of Radial Basis Function (RBF) approaches, specifically Gaussian and Multiquadric RBFs, compared to Cubic and Adaptive Splines for data imputation in time-series datasets. Three ...
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In this manuscript, we introduce a novel Decision Flow (DF) framework for sampling decisions from a target distribution while incorporating additional guidance from a prior sampler. DF can be viewed as an AI-driven al...
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Photonic devices rarely provide both elaborate spatial control and sharp spectral control over an incoming *** optical metasurfaces,for example,the localized modes of individual meta-units govern the wavefront shape o...
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Photonic devices rarely provide both elaborate spatial control and sharp spectral control over an incoming *** optical metasurfaces,for example,the localized modes of individual meta-units govern the wavefront shape over a broad bandwidth,while nonlocal lattice modes extended over many unit cells support high quality-factor ***,we experimentally demonstrate nonlocal dielectric metasurfaces in the near-infrared that offer both spatial and spectral control of light,realizing metalenses focusing light exclusively over a narrowband resonance while leaving off-resonant frequencies *** devices attain this functionality by supporting a quasi-bound state in the continuum encoded with a spatially varying geometric *** leverage this capability to experimentally realize a versatile platform for multispectral wavefront shaping where a stack of metasurfaces,each supporting multiple independently controlled quasi-bound states in the continuum,molds the optical wavefront distinctively at multiple wavelengths and yet stay transparent over the rest of the *** a platform is scalable to the visible for applications in augmented reality and transparent displays.
The impacts incurred by floods regularly affect the planets population, inflicting social and economic problems. Optimal control strategies based on reservoir management may aid in controlling floods and mitigating th...
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The impacts incurred by floods regularly affect the planets population, inflicting social and economic problems. Optimal control strategies based on reservoir management may aid in controlling floods and mitigating the resulting damage. To this end, an accurate dynamic representation of water systems is needed. In practice, flood control strategies rely on hydrological forecasting models obtained fromconceptual or data-drivenmethods. Encouraged by recent works, this research proposes a novel surrogate model for water flow in a river channel based on physics-informed neural networks (PINNs). This approach achieved promising results regarding the assimilation of real-data measurements and the parameter identification of differential equations that govern the underlying dynamics. This article investigates PINN performance in a simulated environment built directly from a configuration of the Saint-Venant equations. The objective is to create a suitable model with high prediction accuracy and scientifically consistent behavior for use in real-Time applications. The experiments revealed promising results for hydrological modeling and presented alternatives to solve the main challenges found in conventional methods while assisting in synthesizing real-world representations. Impact Statement-The research seeks to contribute to the hydrological modeling area with a surrogate model based on physicsinformed neural networks (PINNs) to water flow in a watershed. In practice, thesemodels use conceptual or *** models to reach the precision provided by themethodology use large numbers of physical parameters. These parameters can demand deep knowledge about the environment and are possibly hard to identify in a complex basin. On the other hand, while data-driven methods do not require such knowledge about the dynamic system, they depend on a reliable and useful database to guarantee the accuracy of system *** introduce PINNs as a viable solution for
In previous work [Phys. Rev. X 5, 021020 (2015)] it was shown that stealthy hyperuniform systems can be regarded as hard spheres in Fourier space in the sense that the structure factor is exactly zero in a spherical r...
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In previous work [Phys. Rev. X 5, 021020 (2015)] it was shown that stealthy hyperuniform systems can be regarded as hard spheres in Fourier space in the sense that the structure factor is exactly zero in a spherical region around the origin in analogy with the pair-correlation function of real-space hard spheres. While this earlier work focused on spatial dimensions d=1–4, here we extend the analysis to higher dimensions in order to make connections to high-dimensional sphere packings and the mean-field theory of glasses. We exploit this correspondence to confirm that the densest Fourier-space hard-sphere system is that of a Bravais lattice in contrast to real-space hard spheres, whose densest configuration is conjectured to be disordered. In passing, we give a concise form for the position of the first Bragg peak. We also extend the virial series previously suggested for disordered stealthy hyperuniform systems to higher dimensions in order to predict spatial decorrelation as a function of dimension. This prediction is then borne out by numerical simulations of disordered stealthy hyperuniform ground states in dimensions d=2–8, which have only recently been made possible due to a highly parallelized algorithm.
Using simplifying assumptions that are related to the time reversal symmetry, a 1-dimensional family of 8-stage pseudo-symplectic Runge–Kutta methods of order (4, 8), i.e., methods of order 4 that preserve symplectic...
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